Finally let’s look at graphs of usage over time, starting with Services:

We can see that usage grew steadily until early 2016, when it stabilised at the current level. Probably something to do with Drupal 8 being released at that time.

And then the graph for REST UI:

We can see a steady and steep rise in usage right from the time Drupal 8 was released.

These figures and graphs seem to confirm that decoupled Drupal is rapidly gaining popularity, although Drupal 8 usage still has not reached Drupal 7 level (see update below). It will be interesting to see for how long this rate of increase in usage will continue.

Update 26 April 2018: It has been suggested that the JSON API module should be included in the figures for Drupal 8, and this is indeed a good suggestion. JSON API is used in decoupled Drupal distributions like Contenta and Reservoir, and there should be very little overlap in REST UI and JSON API usage.

Comments

REST UI is just shows half of the puzzle. JSON API is very popular for decoupling and does not depend on REST. IOW, it's entirely possible (even likely) that a site will be fully decoupled site without enabling REST UI at all. JSON API has 6,341 reported installs, which nearly doubles usage :)

You can also probably tack on the GraphQL module usage statistics to this too. The JSON API module is not required for a decoupled site that is built with GraphQL and it's probably unlikely a site would use both.